Geometry and Topology

Speaker: Eiko Kin, Osaka University, Japan

Title: A construction of pseudo-Anosov braids with small normalized entropies

Date: 05/07/2019

Time: 2:00 PM - 3:00 PM

Place: C304 Wells Hall

We consider pseudo-Anosov braids b. The logarithm of the stretch factor of the pseudo-Anosov braid b is called the entropy. By normalized entropy of b with n strands, we mean the n times (the entropy of b).
Let b_n be a sequence of pseudo-Anosov braids. We say that the sequence b_n has a small normalized entropy
if the number of strands of b_n behaves like n
and the normalized entropy of b_n is bounded from above by a constant which does not depend on n.
We give a construction of sequences of pseudo-Anosov braids having small normalized entropies. As an application, we explain the smallest entropy among skew-palindromic braids with n strands is comparable to 1/n.
This is joint work with Susumu Hirose.